 Borel summation

For a formal inverse-power series ${\sum }_{n\ge 0}{a}_n{z}^{-n-1}$, divide its coefficients by $n!$ to form a Borel transform $\sum a_n{t}^n/n!$ and integrate it against $e^{-zt}$. Singularities on the integration ray require a specified contour prescription. Different lateral contours can produce exponentially small differences and the Stokes phenomenon.